Questions: Solve the equation by factoring. 4 x^2-3 x=0 x=

Solve the equation by factoring. 4 x^2-3 x=0 x=
Transcript text: Solve the equation by factoring. \[ \begin{array}{l} 4 x^{2}-3 x=0 \\ x=\square \end{array} \] Write your answers as a list of
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Solution

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Solution Steps

To solve the equation \(4x^2 - 3x = 0\) by factoring, we first factor out the greatest common factor, which is \(x\). This gives us \(x(4x - 3) = 0\). We then set each factor equal to zero and solve for \(x\).

Step 1: Factor the Equation

We start with the equation: \[ 4x^2 - 3x = 0 \] We can factor out the common term \(x\): \[ x(4x - 3) = 0 \]

Step 2: Set Each Factor to Zero

Next, we set each factor equal to zero:

  1. \(x = 0\)
  2. \(4x - 3 = 0\)
Step 3: Solve for \(x\)

For the second factor, we solve for \(x\): \[ 4x - 3 = 0 \implies 4x = 3 \implies x = \frac{3}{4} \]

Final Answer

The solutions to the equation are: \[ \boxed{x = 0} \quad \text{and} \quad \boxed{x = \frac{3}{4}} \]

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